Problem: Simplify the following expression: $y = \dfrac{-3z - 2}{4z - 4} - \dfrac{4z + 3}{4z - 4}$
Explanation: Since the expressions have the same denominator we simply subtract the numerators: $y = \dfrac{-3z - 2 - (4z + 3)}{4z - 4}$ Distribute the negative sign: $y = \dfrac{-3z - 2 - 4z - 3}{4z - 4}$ Combine like terms: $y = \dfrac{-7z - 5}{4z - 4}$